Is it possible for a neural network to be used to compress data?
The auto-encoder (AE) can be used to learn a compressed representation (a vectorised hash value) of each observation in the training dataset, $z$, which can then be used to later retrieve the original (or similar) observation.

The variational auto-encoder (VAE), a statistical variation of AE, can also be used to generate objects similar to the observations (or inputs) in the training set.

There are other data compressor models, for example, Helmholtz machine, which precedes both the AE and VAE.